There is known in the art a composite cutting-off tool according to U.S.S.R. Inventor's Certificate No. 764,855 issued on Aug. 18, 1977 and published on Sept. 23, 1980. Said prior art tool comprises a holder and a disk cutter member with recesses provided on one of its end faces. The holder and the cutter member are interconnected by means of bushings, each having a projection made on one of its end faces and received in the respective one of the recesses provided on the end face of the cutter member, and wedge-and-screw mechanisms each of which is positioned in the opening of a respective bushing and interacts by the sloping surface of its wedge with the peripheral surface of the cutter member. The prior art tool may only be used to perform operations under conditions of low cutting forces when there occur no considerable bending moments acting upon the cutter member of the tool, in other words, the tool lacks proper rigidity. The low rigidity of the tool is due to the presence of a gap between the holder and bushing after securing the cutter member. The gap is caused by the fact that, in the course of securing the cutter member, the wedge-and-screw mechanism urges the bushing to self-align by turning about its axis.